Stability theorems for Fourier frames and wavelet Riesz bases
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in  and used recently in some applications (see ). In the case of an orthonormal basis, our estimate reduces to Kadec’ optimal 1/4 result. The second application proves that a phenomenon discovered by Daubechies and Tchamitchian  for the orthonormal Meyer wavelet basis (stability of the Riesz basis property under small changes of the translation parameter) actually holds for a large class of wavelet Riesz bases.
Math Subject ClassificationsPrimary 42C15 Secondary 41A30
Keywords and PhrasesFrames Riesz basis nonharmonic series wavelets
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